Two Mathematicians in a Bunker and Existence of Pi
Evgenii Rudnyi
exists independently from the mind
The idea came during discussion on embryophysics list
http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5
Below there is a description of the experiment that one could think of
to check the relationships between Mathematics, Mind and Nature (the MMN
experiment). In my view this could be done as a real experiment (so this
is actually not a thought experiment) provided we find two
mathematicians who agree to sacrifice their life for science. I believe
that this should be not that difficult provided the importance of the
experiment for the modern science.
Let us take a completely isolated bunker where the experiment begins.
The initial conditions are enough so that mathematicians can comfortably
chat for awhile with each other about Pi and prove that it exists.
Eventually the oxygen in the bunker will run over and both
mathematicians die. From a viewpoint of a natural science, we have a
dynamical system that eventually comes to the equilibrium state. I
assume that at the beginning when mathematicians prove that Pi exists we
have a consequence of physical states where Pi exists indeed. If you are
in doubt, please suggest any other physical states where you say that Pi
exists. The goal of the experiment is to establish what happens with Pi
at the end when the system reaches the stationary state.
Because of experimental settings, we can neglect the interaction with
environment and I hope that this could be done even for the quantum
mechanics treatment.
Before the experiment will be perform in real, you can take your bet on
whether Pi is retained after the death of mathematicians or not.
Bruno Marchal
I confess I cannot make any sense of what you say here. What do you
mean by "Pi is retained", how do you verify this (after the death of
the mathematicians)?
Also, what is the initial theory that you have to use to interpret the
experience?
I have no clue of the meaning of "I assume that at the beginning when
mathematicians prove that Pi exists we have a consequence of physical
states where Pi exists indeed". "consequence of physical states where
Pi exists" contains too many vague abuse of languages.
When mathematicians proves that Pi exists, they assume a lot (real
numbers, circles, length of enough smooth curves, set theory, etc.).
Usually, they don't prove that Pi exist, they assume that all Cauchy
sequences define some number, called "real number", and they show that
curves sufficiently smooth have a length definable by such a sequence.
Then they define Pi, by the ratio of the length of a circle with its
diameter, and build the Cauchy sequence defining it.
And also, why those two poor mathematicians have to die? Is not Earth
close enough, and the death of Archimedes enough? (assuming the rest
makes sense).
You might just be joking, perhaps.
Bruno
Evgenii Rudnyi
Actually it is not a joke. I guess it is my first step toward Platonia.
As I am a chemist by background, the problem might be not mathematically
correct indeed. Yet, if you could help, we could improve it in this respect.
The background is as follows. I am a chemist and I am still at the level
of what you refer to as physicalism or mechanism. Before I consider your
theorem, first I would like to understand better in my own terms what
physicalsim and mechanism mean and what are the limits. When you talk
about this, it is too fast for me.
According to a common view in natural sciences, a human being (and hence
mind) has been created during evolution. Right now however, after
following discussion here, I have a problem with mathematics along this
way. Science has been pretty successful with mathematical models in
physics, chemistry and even in biology. Yet, according to my current
view, mathematics has been created by the mankind. Thereafter I have got
suddenly a question, why mathematical models (physical laws) are working
at all to describe the Universe when there was no mind. The mathematics,
it seems, was not there at the times of Big Bang.
We cannot repeat Big Bang to understand this. According to the current
economic situation, it is highly unlikely that taxpayers are ready to
spend money on bigger and bigger particle accelerators. Hence my
proposal. If we cannot repeat Big Bang, then for a relatively small
budget we could make easily a local heat death of a small Universe with
two mathematicians and see what happens with mathematics there. In a
way, we repeat evolution in the reverse direction.
It would be nice to exclude mind out of consideration at all but as this
is impossible my goal was to reduce its role as possible. We know that
mathematics is what mathematicians do. Pi is a nice number and most of
taxpayers have heard about it. In the experiment we could allow
mathematicians to write the prove that Pi exists on a paper, it would be
even simpler. If you think that some other mathematical object would be
nicer, please make your suggestion.
So, at the beginning of the experiment we have mind (two working brains
of mathematicians) and they prove on the paper that a given mathematical
object exists. An open question to discuss is what happens with this
mathematical object at the end of the experiment.
Evgenii
On 04.03.2012 14:39 Bruno Marchal said the following:
Brian Tenneson
I can't give you absolute proof especially when we're going to assume different things (i.e., we live in different paradigms). One thing that gives me a clue about my conclusion is that mathematical objects will not exist any less if humanity were to go extinct. However, arguing that is like arguing for a particular answer to a koan.
Bruno Marchal
On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:
> Bruno,
>
> Actually it is not a joke. I guess it is my first step toward
> Platonia. As I am a chemist by background, the problem might be not
> mathematically correct indeed. Yet, if you could help, we could
> improve it in this respect.
>
> The background is as follows. I am a chemist and I am still at the
> level of what you refer to as physicalism or mechanism.
Hmm... You should read more carefully the post. On the contrary I
claim, and explain, that mechanism and physicalism are incompatible.
I am aware that physicalist, naturalist and materialist tend to use
mechanism as a sort of modern way to put the mind under the rug.
You can see all what I am talking about as an explanation that not
only mechanism does not solve the mind-body problem, but on the
contrary, it leads to the falsity of physicalism and the necessity to
explain where the physical (and physicalist) *belief* come from.
Mechanism entails the negation of physicalism. That's what the UDA is
all about.
The physical reality is not the fundamental reality. The physical
reality will reappear as the way the border of the mathematical
reality looks when seen form inside, from some points of view
(actually the points of view of predicting measurement values).
I can argue that with comp, concerning the basic ontological level, it
is absolutely undecidable if there is anything more than the numbers,
that is 0, the successor of zero, the successor of the successor of
zero, ...
And every lawful thing is deducible from the laws of addition and
multiplication (that you have learn is school, and certainly apply in
chemistry).
So, with mechanism, physics is not the fundamental science. Physics
has to be reduced to digital machine (number) biology, psychology,
theology (given that non provable truth have a big role in the origin
of matter).
> Before I consider your theorem, first I would like to understand
> better in my own terms what physicalsim and mechanism mean and what
> are the limits. When you talk about this, it is too fast for me.
You have to do the thought experiment. You have to admit the
hypothesis, if only for the sake of the argument.
>
> According to a common view in natural sciences, a human being (and
> hence mind) has been created during evolution.
Something like that might be locally correct, but appears to be wrong
in the comp (digital mechanist) theory.
> Right now however, after following discussion here, I have a problem
> with mathematics along this way. Science has been pretty successful
> with mathematical models in physics, chemistry and even in biology.
> Yet, according to my current view, mathematics has been created by
> the mankind. Thereafter I have got suddenly a question, why
> mathematical models (physical laws) are working at all to describe
> the Universe when there was no mind. The mathematics, it seems, was
> not there at the times of Big Bang.
You might confuse mathematics, branch of human science, and the
possible mathematical reality.
The mathematical reality does not depend on the physical reality, and
a large part of it might no depend on the human mind.
For example the fact that 17 is prime, is a mathematical fact which
does not depend on the presence of human. It is just the fact that a
line of 17 distinguishable objects cannot be cut in a finite of part
to be reassembled into a rectangle different from the line itself. For
example 8 is not prime because the line
. . . . . . . .
can be cut and become
. . . .
. . . .
You might convince you experimentally that 17 is prime in this way,
but you can also prove it entirely as a consequence of the laws of
addition and multiplication. No concept of physics enter in this at
all. You might *apparently* need a physical reality to convince a
human being that 17 is prime, but you don't need to refer to it to
transmit the concept of prime number, despite it can helps for the
intuition, like above.
>
> We cannot repeat Big Bang to understand this.
Remember that we (try) to be scientist, meaning that we cannot commit
ourself ontologically, except by making clear our postulate. The big-
bang theory is a theory, an hypothesis, which usually assume an
ontological (primitively existing) universe.
With mechanism, that theory is already refuted by UDA+MGA.
What is the big bang, then. Open problem. Most plausibly a first
person plural sharable computational state of some universal number.
> According to the current economic situation, it is highly unlikely
> that taxpayers are ready to spend money on bigger and bigger
> particle accelerators. Hence my proposal. If we cannot repeat Big
> Bang, then for a relatively small budget we could make easily a
> local heat death of a small Universe with two mathematicians and see
> what happens with mathematics there. In a way, we repeat evolution
> in the reverse direction.
I can see you don't like mathematician!
:)
>
> It would be nice to exclude mind out of consideration at all but as
> this is impossible my goal was to reduce its role as possible. We
> know that mathematics is what mathematicians do.
Some constructivist mathematicians might agree, but most
mathematicians consider that they explore territories. They consider
that they make discoveries. Most discoveries are unexpected.
especially after Gödel, it is hard to defend a conventionalist
philosophy of math. And the, just to define what could mean
"mechanism", you need to assume that the arithmetical truth is more
primary than the mathematicians, if only to model mechanist
mathematicians by (Löbian) numbers. The you can distinguish the math
produce by the number, and the math of the number.
> Pi is a nice number
But it is a real number. I prefer to exclude them of the ontology,
because they have the same fate as matter. If they have an ontological
existence, it will not change anything in the machine (number)
epistemology. So they are like invisible horses, and with occam, you
can exclude them. Natural numbers will belief in real number,
independently of any of their ontological status.
> and most of taxpayers have heard about it. In the experiment we
> could allow mathematicians to write the prove that Pi exists on a
> paper, it would be even simpler. If you think that some other
> mathematical object would be nicer, please make your suggestion.
It is very weird, here.
>
> So, at the beginning of the experiment we have mind (two working
> brains of mathematicians) and they prove on the paper that a given
> mathematical object exists. An open question to discuss is what
> happens with this mathematical object at the end of the experiment.
Mathematical objects are invariant. Nothing happens to them. Things
can happen to them, in a relative sense, by the intermediate of true
relation bearing on them.
If you divide 8 by 4, this gives 2. But 8 remains untouched by that
operation. It is just that it is true that there exist a number which
multiplied by 4 gives 8, and that such a number is 2 (the nickname for
the successor of the successor of 0).
Mathematical object are structured only by their relations, and this
in a way which does not depend on time, space, animals, humans, or
whatever. Indeed, that is why math is useful to describe atemporally
even temporal relation, by a function of the type y = f(t).
But all questions require a precise theory in the background, and if
what I say don't help, you might think about formalizing a bit more
the background you are using.
Bruno
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Evgenii Rudnyi
mathematics objects exist. In this case Bruno is consistent when he says
that everything is formed from the mathematical objects in Platonia. Do
you mean the same?
I personally still at the position that there are some material objects,
atoms, molecules, crystals, etc., that are independent from the mind. I
believe that this is quite a typical position for natural sciences. Then
it is hard to imagine how mathematical objects coexist with physical
objects. Some sort of dualism?
Evgenii
On 04.03.2012 17:28 Brian Tenneson said the following:
John Mikes
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Craig Weinberg
>
> I personally still at the position that there are some material objects,
> atoms, molecules, crystals, etc., that are independent from the mind.
cosmos then there are going to be a lot of strange conclusions that
come up. Think about the hundreds of billions of galaxies...the
billions of organisms on this planet alone.. were all of them utterly
blind and deaf to their own existence for their entire history until
the moment that Homo sapiens began to take an interest in them from
their home on this remote speck of dust?
"Thereafter I have got suddenly a question, why mathematical models
(physical laws) are working at all to describe the Universe when there
was no mind. "
inertia. Worlds. The more intelligent you are, the more worlds you can
make sense of. The more you can make sense of the motivations and
processes of lesser worlds. As the collective intelligence of our
species has concentrated the knowledge available to each of us, we
gathered meta-perceptual commonalities. Mathematical models are
actually common perception/participation strategies as characterized
by ourselves as outside observers. We are made of matter, so we see
ourselves reflected in a particular way in matter. A way which is both
intimately familiar and alien to us.
The problem is that matter is only half of the story. We are also made
of ourselves. We need mathematical models to plumb the depths of
mysteries which are beyond our own frame of reference. Mysteries that
cut across distant levels like physics and chemistry. The closer we
get to our own level of perception however, the less mathematical
models tell the whole story. Biology, zoology, anthropology,
psychology, all benefit from mathematical models to some extent, but
they fall short of modeling what it is to be alive, to be a person,
etc. Mathematics is by definition an exterior facing manipulation. It
begins by counting on our fingers - an exterior computation which
transforms part of our body to a true set of objects - generic,
recursive, controllable. Our fingers are not a mind. They are the
beginnings of the mind offloading its grunt work onto objects. It is a
way of generalizing part of ourselves to make it seem like it is not
part of ourselves.'
Right now, in the post-Enlightenment era, our success with mathematics
has been so impressive that we have begun to imagine that we ourselves
have a mathematical basis. It is a little like following the counting
of the fingers back into the brain to find where smaller and smaller
fingers are counting. If we try a sense-based model instead, there is
no problem with mathematics being both a high level symbolic
experience within a human cortex as well as indirect experiences of
low level microcosmic events or other events which can be detected and
controlled externally with physical instruments. This is what sense
does. It jumps to conclusions. It ties levels together figuratively.
We want to move our hand, and we just do it. We don't have to
consciously transduce a signal through neural and muscular fibers. We
couldn't find a muscle fiber even if we wanted to.
This is what mathematics does for us, it extends our minds
figuratively outside of our native scale of perception, so that we
can, in a way, make more of the universe part of our figurative body.
Of course, just as we control our limbs without knowing what is really
going on under the skin, we should not mistake our success with
controlling through mathematical models for understanding the truth -
particularly the truth of our own native perceptual frame, which as
much more subtle and non-mathematical potentials. It could well be the
case that introducing our external control schemas into our own world
is having increasingly toxic consequences, draining the significance
out of culture and promoting an unstoppable drone of financial
computation which consumes the whole of civilization. We may find out
that our mastery over our universe has a Sorcerer's Apprentice side
which reduces itself to an automaton even as it automates everything
around it.
Craig
Evgenii Rudnyi
Thanks for your comments. You are right. It is necessary to be more
accurate with terms. I have read about physicalism on SEP and I see that
I do not need mechanism right now. By the way, where I can read about
mechanism? I see nothing on SEP.
Below is a new version of the problem. I have left Pi though.
Evgenii
P.S. I like a lot this quote about physicalism from SEP
"The first thing to say when considering the truth of physicalism is
that we live in an overwhelmingly physicalist or materialist
intellectual culture. The result is that, as things currently stand, the
standards of argumentation required to persuade someone of the truth of
physicalism are much lower than the standards required to persuade
someone of its negation. (The point here is a perfectly general one: if
you already believe or want something to be true, you are likely to
accept fairly low standards of argumentation for its truth.)"
I should confess that it describes my personal feeling very well. Cheers
to philosophers.
----------------------------------------------------------------
An experiment to perform in order to find experimentally what is the
meaning of Pi under the physicalism hypothesis
Version 2.0
*Assumptions*
-------------
I assume physicalism. From SEP
http://plato.stanford.edu/entries/physicalism/
"Physicalism is the thesis that everything is physical, or as
contemporary philosophers sometimes put it, that everything supervenes
on, or is necessitated by, the physical."
"The general idea is that the nature of the actual world (i.e. the
universe and everything in it) conforms to a certain condition, the
condition of being physical. Of course, physicalists don't deny that the
world might contain many items that at first glance don't seem physical
� items of a biological, or psychological, or moral, or social nature.
But they insist nevertheless that at the end of the day such items are
either physical or supervene on the physical."
"Physicalism is sometimes known as �materialism�; indeed, on one strand
to contemporary usage, the terms �physicalism� and �materialism� are
interchangeable."
*Problem*
---------
The Pi number enjoys extensive use in physics. This raises the question
what Pi means under the physicalism hypothesis.
*Experiment*
------------
Below there is a description of the experiment that one could think of
to check the relationships between Pi and physicalism.
Let us take a completely isolated bunker where the experiment begins.
There are two mathematicians in the bunker and the initial conditions
are enough so that mathematicians can comfortably work for awhile and
prove the existence of Pi on a paper. Eventually the oxygen in the
bunker will run over and both mathematicians die.
From a physicalism viewpoint, we have a dynamical system that
eventually comes to the equilibrium state. Because of experimental
settings, we can neglect the interaction with environment and I hope
that this could be done even for the quantum mechanics treatment.
The experiment takes an operational approach to what Pi means. During
the initial stage of the experiment mathematicians prove the existence
of Pi. This should be enough to claim that Pi is present in the bunker
at least for some moments.
*Questions to discuss*
----------------------
How Pi supervenes to the physical states of the bunker with mathematicians?
Is Pi invariant in respect to states of the dynamical system in question
or not?
On 04.03.2012 18:48 Bruno Marchal said the following:
> big-bang theory is a theory, an hypothesis, which usually assume an
> ontological (primitively existing) universe.
>
> With mechanism, that theory is already refuted by UDA+MGA.
>
> What is the big bang, then. Open problem. Most plausibly a first
> person plural sharable computational state of some universal number.
>
>
>
>
>
>> According to the current economic situation, it is highly unlikely
>> that taxpayers are ready to spend money on bigger and bigger
>> particle accelerators. Hence my proposal. If we cannot repeat Big
>> Bang, then for a relatively small budget we could make easily a
>> local heat death of a small Universe with two mathematicians and
>> see what happens with mathematics there. In a way, we repeat
>> evolution in the reverse direction.
>
> I can see you don't like mathematician! :)
>
>
>
>>
>> It would be nice to exclude mind out of consideration at all but as
>> this is impossible my goal was to reduce its role as possible. We
>> know that mathematics is what mathematicians do.
>
> Some constructivist mathematicians might agree, but most
> mathematicians consider that they explore territories. They consider
> that they make discoveries. Most discoveries are unexpected.
> especially after G�del, it is hard to defend a conventionalist
> philosophy of math. And the, just to define what could mean
> "mechanism", you need to assume that the arithmetical truth is more
> primary than the mathematicians, if only to model mechanist
> mathematicians by (L�bian) numbers. The you can distinguish the math
Evgenii Rudnyi
It is not that bad to say that we do not know something. Yet, it might
be even better to specify more accurately what exactly we do not know.
Think of your younger colleagues that do chemistry research right now.
Chemists have been quite successful and the story continues. The
concepts of atom, molecule, macromolecule, electron density, etc. have
helped a lot along this way. We may take this concepts ontologically or
just pragmatically, this is after all not that important. Materials
science seems not to be affected.
Evgenii
On 05.03.2012 00:17 John Mikes said the following:
> Hello, Evgenii, my fellow (former) chemist: I ended up after my 38
> patents in (environmental-polymer) chemistry with an agnosticism, not
> 'believeing' in the atom (don't even mention 'molecules' or the
> macromolecules I created). It is all the figment of the human mind to
> EXPLAIN whatever transpired into our 'model' of presently knowables
> from (some?) infinite complexity - way beyond our imaginative power.
> Maxim: EVERYTHING *does* exist that pops up in the mind, if not
Stephen P. King
This is a very fascinating statement to me and I find John's comments to be very wise! "...it might be even better to specify more accurately what exactly we do not know. " Does it not lead to a paradox? For if we could state exactly what we do not know then it would be the case that we do in fact know it and thus "we would known what we do not know", which appears to be a contradiction.
Is this a sample of a more general kind of situation that is inevitable given the idea of self-reference? It seems to me that we need to consider that Bivalency can be a source of error sometimes, or claim that knowledge is impossible. (note the bivalence here! LOL!) I am focusing on this because it it part of my overall critique of the idea of a Theory of Everything. For example, what exactly does it mean for a sentence to have a definite truth value absent the ability to evaluate that truth value? This is what I see your hypothetical situation as discussing....
Onward!
Stephen
meekerdb
The experiment takes an operational approach to what Pi means. During the initial stage of the experiment mathematicians prove the existence of Pi.
When mathematicians 'prove the existence' of something they are just showing that something which satisfies a certain definition can be inferred from a certain set of axioms.� In your example the mathematicians may define Pi as the ratio of the circumference to the diameter of a circle in Euclidean geometry. But what does that mean if geometry is not Euclidean; and we know it's not since these mathematicians are in the gravitational field of the Earth.� Mathematics is about abstract propositions.� Whether they apply to reality is a separate question.
Brent
Evgenii Rudnyi
> On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
>> The experiment takes an operational approach to what Pi means.
>> During the initial stage of the experiment mathematicians prove the
>> existence of Pi.
>
> When mathematicians 'prove the existence' of something they are just
> showing that something which satisfies a certain definition can be
> mathematicians may define Pi as the ratio of the circumference to the
> diameter of a circle in Euclidean geometry. But what does that mean
> if geometry is not Euclidean; and we know it's not since these
> mathematicians are in the gravitational field of the Earth.
> reality is a separate question.
>
> Brent
>
>
I agree that this assumption might not be the best one. I will think it
over.
However, I do not completely understand you. How the geometry of
physical space in which mathematicians reside influences the definition
of Pi? Mathematicians will consider just Euclidean geometry, that's it.
In my view, whether the physical space Euclidean or not, does not
influence the work of mathematicians.
In any case, the problem remains. What is mathematics under the
assumption of physicalism? Do you have any idea?
Evgenii
meekerdb
Exactly. Hence mathematics =/= reality.
>
> In any case, the problem remains. What is mathematics under the assumption of
> physicalism? Do you have any idea?
It's a language game.
Brent
A physicist goes off to a conference. After a week his suit�s gotten soiled and crumpled,
so he goes out to look for a dry cleaner. Walking down the main street of town, he comes
upon a store with a lot of signs out front. One of them says �Dry Cleaning.� So he goes in
with his dirty suit and asks when he can come back to pick it up. The mathematician who
owns the shop replies, �I�m terribly sorry, but we don�t do dry cleaning.� �What?�
exclaims the puzzled physicist. �The sign outside says �Dry Cleaning�!� �We do not do
anything here,� replies the mathematician. �We only sell signs!�
--- Alain Connes, in Changeux
>
> Evgenii
>
Jason Resch
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
It's a language game.
In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?
Brent
A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”
--- Alain Connes, in Changeux
Evgenii
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meekerdb
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality; but that was what the bunker thought experiment was intended to test.� You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
Brent
�
It's a language game.
In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?
This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. �Mathematical truth�transcends the�symbol manipulation game defined by any set of axioms.
Jason�Brent
A physicist goes off to a conference. After a week his suit�s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says �Dry Cleaning.� So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, �I�m terribly sorry, but we don�t do dry cleaning.� �What?� exclaims the puzzled physicist. �The sign outside says �Dry Cleaning�!� �We do not do anything here,� replies the mathematician. �We only sell signs!�
--- Alain Connes, in Changeux
Evgenii
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Jason Resch
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
Okay.
but that was what the bunker thought experiment was intended to test.
I fail to see how the bunker experiment tests this. The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed. Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics. If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe. Further, there is a growing collection of evidence that in most universes, conscious life is impossible. This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence. Just because one proposed test will not work should not imply a theory is untestable.
A final thought: Consider what our universe would look like if you were a being outside it. You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe. You could not see the stars or galaxies of our universe, for photons never leave it. There would be no relativity of size, or time, or distance between your perspective and that within our universe. You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended. You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws. In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object. From the outside, one could study our universe through the window of math and computer simulation, but observation through your senses or any measurement apparatus would never reveal its existence.
Jason
Brent
It's a language game.
In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?
This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. Mathematical truth transcends the symbol manipulation game defined by any set of axioms.
JasonBrent
A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”
--- Alain Connes, in Changeux
Evgenii
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No virus found in this message.
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Version: 2012.0.1913 / Virus Database: 2114/4852 - Release Date: 03/05/12
meekerdb
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
Okay.
�but that was what the bunker thought experiment was intended to test.�
I fail to see how the bunker experiment tests this.� The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
�
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.� Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.�
That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.� What is computable is much less than all mathematics.
If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.� Further, there is a growing collection of evidence that in most universes, conscious life is impossible.
There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.� In any case it doesn't warrant the conclusion that all possible universes exist.
� This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.� Just because one proposed test will not work should not imply a theory is untestable.
A final thought: Consider what our universe would look like if you were a being outside it.� You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.� You could not see the stars or galaxies of our universe, for photons never leave it.� There would be no relativity of size, or time, or distance between your perspective and that within our universe.� You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.� You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.� In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.
That's a complete non sequitur.
� From the outside, one could study our universe through the window of math and computer simulation,
I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.
Brent
Jason Resch
On 3/5/2012 8:28 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
Okay.
but that was what the bunker thought experiment was intended to test.
I fail to see how the bunker experiment tests this. The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed. Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.
The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist. I find the existence of all consistent structures to be a simpler theory. If the integers can exist, why cant the Mandlebrot set, or the Calabi–Yau manifolds?
If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe. Further, there is a growing collection of evidence that in most universes, conscious life is impossible.
There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.
In Bruno's theory, "physical universes" are considered observations of minds. Where I use the term, I refer to independent structures (both seen and unseen).
In any case it doesn't warrant the conclusion that all possible universes exist.
No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one. Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.
There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there. I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false. So tell me: for what reason(s) do you reject the hypothesis?
This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence. Just because one proposed test will not work should not imply a theory is untestable.
A final thought: Consider what our universe would look like if you were a being outside it. You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe. You could not see the stars or galaxies of our universe, for photons never leave it. There would be no relativity of size, or time, or distance between your perspective and that within our universe. You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended. You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws. In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.
That's a complete non sequitur.
From the outside, one could study our universe through the window of math and computer simulation,
I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.
Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes. Different universes are independent in such a way that we can only access them as we access all other mathematical structures. Also, if your model is perfect, there should be no difference between studying the model and the object it represents. In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.
That we cannot affect them from our current location does not make them any less real. That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real, that our experiences don't matter, or that the existence of the structure that is our universe is without consequence. Immutability says nothing about an objects reality; we cannot affect the past, or portions of our universe sufficiently far away, yet most would say these exist. Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us. There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away. The existence of all structures reconfirms, in a stronger senses, quantum immortality. If all the other universes are out there, then given mechanism, a we are all immortal. Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.
Jason
Brent
meekerdb
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line.� So no matter what they measure in their bunker it will be consistent with one or the other.� So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. �You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
Okay.
�but that was what the bunker thought experiment was intended to test.�
I fail to see how the bunker experiment tests this.� The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
�
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation.� What is computable is much less than all mathematics.
People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed.� Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.�
The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist.�
That they are observationally indistinguishable is vacuously satisfied by them both being unobservable.
I find the existence of all consistent structures to be a simpler theory.� If the integers can exist, why cant the Mandlebrot set, or the Calabi�Yau manifolds?
I didn't say that things descriable by those mathematics *can't* exist.� I just said I don't believe they do.� Yaweh *could* exist (and according to you does) but I don't believe he does.
�There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.�
If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe.� Further, there is a growing collection of evidence that in most universes, conscious life is impossible.
In Bruno's theory, "physical universes" are considered observations of minds.�
Hmm? Is that right?� The UD* certainly must generate lots of programs without human-like consciousness, e.g. this universe in which dinosaurs weren't killed off.� So I'm not clear on why there wouldn't be infinitely many universes without conscious beings.
Where I use the term, I refer to independent structures (both seen and unseen).
�
In any case it doesn't warrant the conclusion that all possible universes exist.
No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one.�
Maybe I'm not understanding what you mean by "independent structures".� Independent of what?� I don't see that referring to independent structures has anything to do with whether they exist.
Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.
There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there.� I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false.� So tell me: for what reason(s) do you reject the hypothesis?
I don't reject it; I just don't accept it.� It seems to ill defined to be testable.
�
� This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence.� Just because one proposed test will not work should not imply a theory is untestable.
A final thought: Consider what our universe would look like if you were a being outside it.� You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe.� You could not see the stars or galaxies of our universe, for photons never leave it.� There would be no relativity of size, or time, or distance between your perspective and that within our universe.� You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended.� You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws.� In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.
That's a complete non sequitur.
� From the outside, one could study our universe through the window of math and computer simulation,
I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.
Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes.� Different universes are independent in such a way that we can only access them as we access all other mathematical structures.�
Ask yourself WHY they are inaccessible.� Isn't it because if they were accessible then there would be contradictory facts in the world.� And why can't there be contradictory facts?� Because ex falso quodlibet.� But "quodlibet" is what has already been hypothesized. (on the other hand see Graham Priest's "In Contradiction").
Also, if your model is perfect, there should be no difference between studying the model and the object it represents.� In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.
Except if we are studying them or simulating them, then we can interact with them and (necessarily?) change them.
That we cannot affect them from our current location does not make them any less real.�
"Affect" and "observe" are two different things (at least classically) and if we can neither affect or observe that makes them rather like Russell's teapot.� We can't be sure it doesn't exist, but there's no reason to think it does.
That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real,
that our experiences don't matter, or that the existence of the structure that is our universe is without consequence.� Immutability says nothing about an objects reality; we cannot affect the past,
Unless the past was identical with the present then something has mutated.
or portions of our universe sufficiently far away, yet most would say these exist.� Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us.� There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away.
So you say, but I'm betting not...and so are you.
The existence of all structures reconfirms, in a stronger senses, quantum immortality.� If all the other universes are out there, then given mechanism, a we are all immortal.� Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.
I'm not sure I've survived the past year.
Brent
The person I was when I was 3 years old is dead. He died because
too much new information was added to his brain.
�������� -- Saibal Mitra
acw
>>>> whole
>>>> (such as the local part of this universe) with another subset of the
>>>> whole
>>>> (euclidean geometry), and decide that the whole (of mathematics) is
>>>> different
>>>> from the whole (of reality).
>>>
>>> The same mathematicians in the same place could 'prove the existence'
>>> of the
>>> meeting point of parallel lines or that through a point there is more
>>> than one
>>> their bunker
>>> it will be consistent with one or the other. So you can only hold that
>>> mathematics=reality if you assume everything not self-contradictory
>>> exists in
>>> reality;
>>>
>>>
>>> Okay.
>>>
>>>
>>>
>>> experiment seems to
>>> assume that mathematical reality is or depends upon a physical
>>> representation.
>>>
>>> HERE but
>>> somewhere (Platonia?) it's really true.
>>>
>>>
>>> People used to say Darwin's theory was untestable, because evolution
>>> was such a
>>> list have
>>> argued that the hypothesis has already survived one test: the
>>> unpredictability in
>>> quantum mechanics.
>>
>> universes are
>> mathematics.
>>
>>
>> The existence of all mathematical structures implies the existence of
>> all programs, which is observationally indistinguishable from Bruno's
>> result taking only the integers to exist.
>
> by them both being unobservable.
>
>> I find the existence of all consistent structures to be a simpler
>> Calabi�Yau manifolds?
>
> I didn't say that things descriable by those mathematics *can't* exist.
> to you does) but I don't believe he does.
>
contradictory properties is a strawman.
>>
>>
>>> If instead we found our environment and observations of it to be
>>> perfectly
>>> deterministic, this would have ruled out mechanism+a single or finite
>>> most universes,
>>> conscious life is impossible.
>>
>> There's a popular idea that most possible universes are inhospitable
>> to conscious
>> life: a theory that might well be false under Bruno's hypothesis in which
>> consciousness and universes are both realized by computation.
>>
>>
>> minds.
>
> without human-like consciousness, e.g. this universe in which dinosaurs
> many universes without conscious beings.
>
>
like in-a-moment experience with very few memories or continuity.
Consciousness should not be confused with
self-awareness/self-consciousness. A mathematical object with no
conscious observer has no one to see it from the inside, thus it's
merely abstract (but for a mathematical monist or a non-eliminitavist
computationalist that would just be a program or structure empty of
observers). Of course, said structure could also find itself studied by
mathematicians, or simulated on computers or merely within other
structures (such as observer physical objects).
>> Where I use the term, I refer to independent structures (both seen and
>> unseen).
>>
>> universes exist.
>>
>>
>> No, it doesn't prove they all exist, just that there are perhaps
>> infinitely many universes almost exactly like this one.
>
> structures has anything to do with whether they exist.
>
>> Which, while not proving everything exists, is certainly something we
>> would expect to find if indeed everything exists.
>
> Of course it is trivial to say that an everything theory successfully
> whether it does the converse. Can it predict that we don't see some
> (almost all) things.
>
I'd say that it could. A theory like COMP predicts many possibilities
outside any modern physical theories, some such things are very much
testable, but not falsifiable (because the only way we have of testing
something is by observing it and if we are part of the experiment, that
leads to tricky philosophy of science problems, which can be remedied by
thinking of reality as shared computations by a large population of
observers, not an inescapable 3p reality).
If this world was a Harry Potter magical irreducible universe or
something equally weird like purely Newtonian physics, yet with physical
(non-simulated brain), I would say that could refute COMP. Why? COMP
leads to an increase of possible continuations and so do other
everything-theories. Which essentially means that if such a theory is
true then certain types of experiences are more probable than others,
while others are utterly unlikely (but not impossible). This is yet
another way to test these types of theories.
>>
>> There are all these reasons and arguments that are compatible with and
>> suggestive of the idea that all is out there. I haven't seen one
>> offered piece of evidence from you that would suggest the idea of
>> mathematical reality is false. So tell me: for what reason(s) do you
>> reject the hypothesis?
>
> I don't reject it; I just don't accept it. It seems to ill defined to be
> testable.
>
I find it 'everything' theories more plausible than 'something' theories
- why? Ask the question "why these particlar laws of physics?" or "is
there any reason to suppose only this box in which we happen to be
exists and no other boxes which we have not observed exist?". The
'everything' theory is always simpler by Occam or other heuristics which
prefer theories of reduced complexity. The Jahweh 'theory' has way too
high complexity.
A skeptical person would not believe anything they did not experience,
but then their position would be irrealist or merely instrumental - they
refuse to try and guess what's underneath and only predict by their
experience and nothing more. A realist (but sometimes also monist or
even idealist) position would assume that something is going on
underneath and understand what it is instead of just refusing to ask
that question.
>>
>>> This can also be considered as confirmation of the theory that there
>>> exists a
>>> huge diversity in structures that have existence. Just because one
>>> proposed test
>>> will not work should not imply a theory is untestable.
>>>
>>> A final thought: Consider what our universe would look like if you
>>> were a being
>>> outside it. You would not be affected by the gravity of objects in
>>> our universe,
>>> for gravity only affects physical objects in this universe. You could
>>> not see the
>>> stars or galaxies of our universe, for photons never leave it. There
>>> would be no
>>> relativity of size, or time, or distance between your perspective and
>>> that within
>>> our universe. You could not say what time it happened to be in our
>>> universe, or
>>> whether the world had even formed yet or long ago ended. You could in
>>> no way make
>>> your presence known to us in this universe, for our universe is bound
>>> to follow
>>> certain fixed laws. In summary, outside our universe there is no
>>> evidence we even
>>> exist; our entire universe is merely an abstract, immutable and timeless
>>> mathematical object.
>>
>> That's a complete non sequitur.
>>
>>
>>> From the outside, one could study our universe through the window of
>>> math and
>>> computer simulation,
>>
>> I could study a mathematical or computational representation, but
>> that's not the
>> same as studying our universe - unless you beg the question.
>>
>>
>> Clearly we will not get proof of the mathematical universe hypothesis
>> by seeing other universes and mathematical objects through telescopes.
>> Different universes are independent in such a way that we can only
>> access them as we access all other mathematical structures.
>
> Ask yourself WHY they are inaccessible. Isn't it because if they were
> accessible then there would be contradictory facts in the world. And why
> can't there be contradictory facts? Because ex falso quodlibet. But
> "quodlibet" is what has already been hypothesized. (on the other hand
> see Graham Priest's "In Contradiction").
>
>> Also, if your model is perfect, there should be no difference between
>> studying the model and the object it represents. In the future, we
>> will be able to discover, emulate, and visit other universes by
>> discovering them in math, and using sufficiently powerful simulations,
>> know what it is like there, or whether or not life is possible.
>
> Except if we are studying them or simulating them, then we can interact
> with them and (necessarily?) change them.
>
Changing them means looking at different structure than before - either
at the structure including your changes or the structure in which you're
contained and the inner structure you're simulating.
Interacting with something means they are within the same structure.
Observing merely means simulation or inference.
>>
>> That we cannot affect them from our current location does not make
>> them any less real.
>
> "Affect" and "observe" are two different things (at least classically)
> and if we can neither affect or observe that makes them rather like
> Russell's teapot. We can't be sure it doesn't exist, but there's no
> reason to think it does.
>
There are far better reasons to consider 'everything'-type theories.
Most people don't care about theories about unicorns and ponies, but
they do care about theories about why we exist or why physics behaves
like this or that or why we have this or that experience.
>> That our universe is an immutable, abstract, timeless object to a
>> being in a different universe does not imply we are any less real,
>
> I'm not sure what being "an abstract object to a being" means, but I
> don't think it implies we are any more real.
>
>> that our experiences don't matter, or that the existence of the
>> structure that is our universe is without consequence. Immutability
>> says nothing about an objects reality; we cannot affect the past,
>
> Unless the past was identical with the present then something has mutated.
>
>> or portions of our universe sufficiently far away, yet most would say
>> these exist. Moreover, that other universes are currently inaccessible
>> to us does not necessarily imply that they will always be immutable
>> and inaccessible to us. There is always some non-zero possibility that
>> when you wake up tomorrow, you won't find yourself in this universe,
>> but one very far away.
>
> So you say, but I'm betting not...and so are you.
>
What if you find yourself in a situation which greatly reduces your
measure? I would say that would be grounds for unusual expectations.
There's also a variety of thought experiments (some eventually
realisable as actual experiments) which would let you test at least COMP
or MWI (partially).
>> The existence of all structures reconfirms, in a stronger senses,
>> quantum immortality. If all the other universes are out there, then
>> given mechanism, a we are all immortal. Unlike the immortality implied
>> by quantum immortality, we can even survive destruction of this
>> universe, waking up in a different one where the present one was just
>> a very long dream.
>
> I'm not sure I've survived the past year.
>
I would partially agree with you here (especially with the ending
quote). I don't bet on a very strong continuity myself. I change each
passing moment, and I experience discontinuity while sleeping or
otherwise being unconscious. However, as most humans we have
*expectations* and we unconsciously have such inductive beliefs in a
continuity, and we consciously predict and model some of our
experiences. Some may say that subjective probabilities are a mess and
we shouldn't do them (and thus also ignore UDA/COMP), but I believe in
my own subjective experience (I can't doubt it, although I can see why
eliminativist theories are consistent if we ignore the mind) and I do
know that I care about my future subjective experiences. If you really
want a more precise definition of what 1p-you is, imagine an infinite
directed graph where edges are Observer Moments and this 1p-'you' (or a
history) is like a partial path between 2 points (with some small
length, always losing some of the past and gaining some of the future,
like a fuzzy sliding-window). Taking the disconnected OMs view does not
make as much sense for a creature that cares about their future states
and has mostly correct local expectations (consciously known or not).
> Brent
> The person I was when I was 3 years old is dead. He died because
> too much new information was added to his brain.
> -- Saibal Mitra
>
Evgenii Rudnyi
The life is full of paradoxes. My point was that while philosophers
cannot solve apparently simple problems (well, these problems happen not
to be simple), engineers continue doing their business successfully. How
they do it? I believe, exactly this way, they try to understand what
they do not know. Then they make trials, run tests, etc. and finally
with some luck we get a new technology. Whether the theory of everything
exists or not, happens not be essential for the success in engineering.
I do not know why.
Right now I am at the end of Beweistheorien (Proof Theories) by Prof Hoenen
http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24
At the end of his course, he considers the ontological arguments where
the goal was to proof existence from pure logic. A pretty interesting
attempt. Still there is a huge gap between logic and existence and it
seems that engineers successfully fills it. Ask them, how they do it.
Evgenii
On 05.03.2012 14:34 Stephen P. King said the following:
> On 3/5/2012 7:01 AM, Evgenii Rudnyi wrote:
>> John,
>>
>> It is not that bad to say that we do not know something. Yet, it might
>> be even better to specify more accurately what exactly we do not know.
>>
>> Think of your younger colleagues that do chemistry research right now.
>> Chemists have been quite successful and the story continues. The
>> concepts of atom, molecule, macromolecule, electron density, etc. have
>> helped a lot along this way. We may take this concepts ontologically
>> or just pragmatically, this is after all not that important. Materials
>> science seems not to be affected.
>>
>> Evgenii
...
> Hi Evgenii,
>
> This is a very fascinating statement to me and I find John's comments to
> be very wise! "...it might be even better to specify more accurately
> what exactly we do not know. " Does it not lead to a paradox? For if we
> could state exactly what we do not know then it would be the case that
> we do in fact know it and thus "we would known what we do not know",
> which appears to be a contradiction.
> Is this a sample of a more general kind of situation that is inevitable
> given the idea of self-reference? It seems to me that we need to
> consider that Bivalency
> <http://en.wikipedia.org/wiki/Principle_of_bivalence> can be a source of
Bruno Marchal
What most mathematicians believe is that mathematics are the laws true
in all physical universes. And physics is true in one physical universe.
But with the mechanist hypothesis, we know better: the physical laws
are invariant in all numbers' dreams, and physical universe are shared
computations. This explains also (not directly) the non sharable
truth, the contingent one, etc.
The advantage is that we can explain both quanta and qualia, without
postulating a physical, nor a mental realm, just by listening to the
machine, and not taking them for zombie.
It hurts our intuition, today, but science always do that, since its
claim that the earth is not the center of reality. With comp we can
even understand why science has to hurt machine's intuition.
So a physicalist has just to find non mechanist theory of mind, if we
want the physical universe to be ontological (existing in some primary
sense).
Bruno
Evgenii Rudnyi
The danger to society comes not from mathematicians, rather it could
come from technologists. Recently I have read
Jaron Lanier, You Are Not a Gadget: A Manifesto
and the author shows that the society should pay more attention to what
Silicon Valley geeks are silently doing. Just one quote
"Ideals are important in the world of technology, but the mechanism by
which ideals influence events is different than in other spheres of
life. Technologists don't use persuasion to influence you - or, at
least, we don't do it very well. There are a few master communicators
among us (like Steve Jobs), but for the most part we aren't particularly
seductive."
"We make up extensions to your being, like remote eyes and ears
(web-cams and mobile phones) and expanded memory (the world of details
you can search for online). These become the structures by which you
connect to the world and other people. These structures in turn can
change how you conceive of yourself and the world. We tinker with your
philosophy by direct manipulation of your cognitive experience, not
indirectly, through argument. It takes only a tiny group of engineers to
create technology that can shape the entire future of human experience
with incredible speed. Therefore, crucial arguments about the human
relationship with technology should take place between developers and
users before such direct manipulations are designed. This book is about
those arguments."
As for sensations, I do not know. Yesterday after I have read your
email, I went to an Italian restaurant. A small dinner, actually I
wanted just a glass of good red Italian wine, but then I took also a
small plate of cheese assorti with a couple of salad leaves, pepperoni
and bread. I have enjoyed my dinner. Whether wine, bread, cheese, salad
and pepperoni have enjoyed it too, I do not know. I would not mind, if
they did.
Evgenii
On 05.03.2012 06:33 Craig Weinberg said the following:
Bruno Marchal
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:On 05.03.2012 18:29 meekerdb said the following:On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:The experiment takes an operational approach to what Pi means.During the initial stage of the experiment mathematicians prove theexistence of Pi.When mathematicians 'prove the existence' of something they are justshowing that something which satisfies a certain definition can beinferred from a certain set of axioms. In your example themathematicians may define Pi as the ratio of the circumference to thediameter of a circle in Euclidean geometry. But what does that meanif geometry is not Euclidean; and we know it's not since thesemathematicians are in the gravitational field of the Earth.Mathematics is about abstract propositions. Whether they apply toreality is a separate question.BrentI agree that this assumption might not be the best one. I will think it over.However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
Exactly. Hence mathematics =/= reality.
In any case, the problem remains. What is mathematics under the assumption of physicalism? Do you have any idea?
It's a language game.
A physicist goes off to a conference. After a week his suit’s gotten soiled and crumpled, so he goes out to look for a dry cleaner. Walking down the main street of town, he comes upon a store with a lot of signs out front. One of them says “Dry Cleaning.” So he goes in with his dirty suit and asks when he can come back to pick it up. The mathematician who owns the shop replies, “I’m terribly sorry, but we don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign outside says ‘Dry Cleaning’!” “We do not do anything here,” replies the mathematician. “We only sell signs!”
--- Alain Connes, in Changeux
Bruno Marchal
On 06 Mar 2012, at 12:22, Evgenii Rudnyi wrote:
> Stephen,
>
> The life is full of paradoxes. My point was that while philosophers
> cannot solve apparently simple problems (well, these problems happen
> not to be simple), engineers continue doing their business
> successfully. How they do it? I believe, exactly this way, they try
> to understand what they do not know. Then they make trials, run
> tests, etc. and finally with some luck we get a new technology.
> Whether the theory of everything exists or not, happens not be
> essential for the success in engineering. I do not know why.
>
> Right now I am at the end of Beweistheorien (Proof Theories) by Prof
> Hoenen
>
> http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24
>
> At the end of his course, he considers the ontological arguments
> where the goal was to proof existence from pure logic.
This is weird. Since the failure of Whitehead and Russell, it is
admitted that we cannot prove existence, even of the number zero, from
logic alone.
> A pretty interesting attempt. Still there is a huge gap between
> logic and existence and it seems that engineers successfully fills
> it. Ask them, how they do it.
This is weirder. Engineers prove that things exist, in theory which
assume that some things exist. That is not different than proving the
existence of prime or universal number or relation, from the
assumption of the existence of the numbers. It is always relative
proof of existence.
Bruno
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Bruno Marchal
On 3/5/2012 8:28 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 4:57 PM, Jason Resch wrote:
On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meek...@verizon.net> wrote:
On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:Exactly. Hence mathematics =/= reality.
On 05.03.2012 18:29 meekerdb said the following:
On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:
The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove the
existence of Pi.
When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.
Brent
I agree that this assumption might not be the best one. I will think it over.
However, I do not completely understand you. How the geometry of physical space in which mathematicians reside influences the definition of Pi? Mathematicians will consider just Euclidean geometry, that's it. In my view, whether the physical space Euclidean or not, does not influence the work of mathematicians.
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality;This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
Okay.
but that was what the bunker thought experiment was intended to test.
I fail to see how the bunker experiment tests this. The bunker experiment seems to assume that mathematical reality is or depends upon a physical representation.
You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
People used to say Darwin's theory was untestable, because evolution was such a slow process they thought it could never be observed. Some on this list have argued that the hypothesis has already survived one test: the unpredictability in quantum mechanics.
That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
If instead we found our environment and observations of it to be perfectly deterministic, this would have ruled out mechanism+a single or finite universe. Further, there is a growing collection of evidence that in most universes, conscious life is impossible.
There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation.
In any case it doesn't warrant the conclusion that all possible universes exist.
This can also be considered as confirmation of the theory that there exists a huge diversity in structures that have existence. Just because one proposed test will not work should not imply a theory is untestable.
A final thought: Consider what our universe would look like if you were a being outside it. You would not be affected by the gravity of objects in our universe, for gravity only affects physical objects in this universe. You could not see the stars or galaxies of our universe, for photons never leave it. There would be no relativity of size, or time, or distance between your perspective and that within our universe. You could not say what time it happened to be in our universe, or whether the world had even formed yet or long ago ended. You could in no way make your presence known to us in this universe, for our universe is bound to follow certain fixed laws. In summary, outside our universe there is no evidence we even exist; our entire universe is merely an abstract, immutable and timeless mathematical object.
That's a complete non sequitur.
From the outside, one could study our universe through the window of math and computer simulation,
I could study a mathematical or computational representation, but that's not the same as studying our universe -
unless you beg the question.
Evgenii Rudnyi
>
> On 06 Mar 2012, at 12:22, Evgenii Rudnyi wrote:
>
>> Stephen,
>>
>> The life is full of paradoxes. My point was that while philosophers
>> cannot solve apparently simple problems (well, these problems happen
>> not to be simple), engineers continue doing their business
>> successfully. How they do it? I believe, exactly this way, they try to
>> understand what they do not know. Then they make trials, run tests,
>> etc. and finally with some luck we get a new technology. Whether the
>> theory of everything exists or not, happens not be essential for the
>> success in engineering. I do not know why.
>>
>> Right now I am at the end of Beweistheorien (Proof Theories) by Prof
>> Hoenen
>>
>> http://www.podcasts.uni-freiburg.de/podcast_content?id_content=24
>>
>> At the end of his course, he considers the ontological arguments where
>> the goal was to proof existence from pure logic.
>
> This is weird. Since the failure of Whitehead and Russell, it is
> admitted that we cannot prove existence, even of the number zero, from
> logic alone.
>
I have meant the history of such an attempt. It is interesting to learn
how people have tried it and in what context. It was new for me.
>
>> A pretty interesting attempt. Still there is a huge gap between logic
>> and existence and it seems that engineers successfully fills it. Ask
>> them, how they do it.
>
> This is weirder. Engineers prove that things exist, in theory which
> assume that some things exist. That is not different than proving the
> existence of prime or universal number or relation, from the assumption
> of the existence of the numbers. It is always relative proof of existence.
Strictly speaking you are right. What I wanted to say is that engineers
do not care about this but this does not prevent them from doing useful
things. So in a way it is working.
Evgenii
> Bruno
>
>
Bruno Marchal
OK.
>
>>
>>> A pretty interesting attempt. Still there is a huge gap between
>>> logic
>>> and existence and it seems that engineers successfully fills it. Ask
>>> them, how they do it.
>>
>> This is weirder. Engineers prove that things exist, in theory which
>> assume that some things exist. That is not different than proving the
>> existence of prime or universal number or relation, from the
>> assumption
>> of the existence of the numbers. It is always relative proof of
>> existence.
>
> Strictly speaking you are right. What I wanted to say is that
> engineers do not care about this but this does not prevent them from
> doing useful things. So in a way it is working.
OK, but be careful not to become an instrumentalist, which, to be
short, defines roughly truth by useful.
The problem is that the notion of useful is subject dependent. In that
sense, a proposition like "cannabis is dangerous" might be decided to
be true, because it will work very well for a (large) category of
persons (like pharmaceutical lobbies, jail lobbies, textile lobbies,
steel lobbies, wood based paper lobbies, the underground untaxed
economy, the children (who will find it everywhere and will not need
to show the ID).
Lies work very well, for some term, for some people, but it can deform
truth, if that exists, and led science and eventually everyone go
astray. Instrumentalism leads to manipulism, or gangsterism. It leads
to the confusion between truth and power.
Bruno
meekerdb
It's a language game.
The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of mathematics.
But "language" says something.� It says mathematics is about description.
Brent
meekerdb
That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it in the form of "yes doctor", which means that there exist a level such that my consciousness remains unchanged for a digital functional substitution done at that level.
And then the reasoning shows that the physical universe(s), are not generated by any computation. Computations generated my consciousness, and the physical universe is what my consciousness can predict from the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1 part of arithmetic).
If I had written universes are indirectly generated by computation, would that have reflected your view? The only catch I see is that you wrote "can predict" instead of "must predict". Are you allowing for some agency here?
Brent
Bruno Marchal
On 3/6/2012 5:54 AM, Bruno Marchal wrote:That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it in the form of "yes doctor", which means that there exist a level such that my consciousness remains unchanged for a digital functional substitution done at that level.
And then the reasoning shows that the physical universe(s), are not generated by any computation. Computations generated my consciousness, and the physical universe is what my consciousness can predict from the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1 part of arithmetic).
If I had written universes are indirectly generated by computation, would that have reflected your view?
The only catch I see is that you wrote "can predict" instead of "must predict". Are you allowing for some agency here? m
Bruno Marchal
On 3/6/2012 4:26 AM, Bruno Marchal wrote:It's a language game.
The word "game" is so fuzzy that this says nothing at all. Game theory is a branch of mathematics.
But "language" says something. It says mathematics is about description.
Craig Weinberg
> Craig,
>
> The danger to society comes not from mathematicians, rather it could
> come from technologists.
hospital administrators, insurance companies, investment banks,
attorneys, judges, governments, etc who feel compelled to apply
mathematical-seeming solutions to all human problems.
> Recently I have read
>
> Jaron Lanier, You Are Not a Gadget: A Manifesto
wine and cheese, but really, not much more than it is hard to imagine
billions of organisms and molecules being there instead of what we
think we see and taste. Not sure whether the bread knows the
difference between being on a plate or in a stomach, but I have less
of a problem imagining that the cells of our tongue and stomach are
sharing a bit of celebratory feelings with our brain at having eaten
them
Craig.
Stephen P. King
On 06 Mar 2012, at 17:53, meekerdb wrote:
On 3/6/2012 5:54 AM, Bruno Marchal wrote:That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it in the form of "yes doctor", which means that there exist a level such that my consciousness remains unchanged for a digital functional substitution done at that level.
And then the reasoning shows that the physical universe(s), are not generated by any computation. Computations generated my consciousness, and the physical universe is what my consciousness can predict from the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1 part of arithmetic).
If I had written universes are indirectly generated by computation, would that have reflected your view?
Better.But the presence of the word "generated" might still lead to confusion in this setting. Universe(s) are only observed, It is, or they are the 'natural solution' of the comp diophantine measure problem, which bear on the first person.
The only catch I see is that you wrote "can predict" instead of "must predict". Are you allowing for some agency here? mI allow for agency, but not at that level. Indeed Matter, but matter only, is what the mind cannot act on. But the mind can act on the mind, and agency emerges at higher levels.
Why does it seem that you are tacitly accepting the definition of matter as a "substance" as Descartes did in his substance dualism? If matter is an appearance (and not a substance), does this not allow a form of "mind acting on matter"? One only need to consider that the selection process whereby the "next" state in time of a configuration of matter is done by a computation.
A real example of this idea is implemented in the generation of MMORPG games that are very popular. Consider the Bostrom-like question: Since we cannot prove that our physical reality is not a MMORPG virtual world, should we not bet that it actually is? One test for this question is to consider the upper bounds on the ability to detect differences in features at smaller and smaller scales. If, for example, space-time is "granular" then this would almost certainly prove that our physical world is isomorphic to a MMORPG. This idea would be compatible with COMP if we can identify the "players of the MMORPG" with the individual Löbian machines.
Given that some very resent observations of ultra-high energy gamma photons indicate that space-time is not granular, we need a more sophisticated theory to get the idea to work.
No. The reason why "my consciousness" can predict, as opposed to "must predict", is the first person indeterminacy. It is the fact that I cannot know which machine I am, nor which computations executes the relevant states.
We can have partial information set, like, assuming bla-bla-bla, if I am duplicate in {W, M}, I will feel to be in M or in W. That is disjuncts. But by UDA-(step 8 included), I have to say at each instant I will be in u1, u2, u3, u4, ... that is the infinite sequence of programs generating my current state. They all compete in the measure, and "we" can only see the result of that from inside. Here the 1p and its invariance for the delays explains that such "results" never appear in the UD, but is on the border of UD*.
Onward!
Stephen
Pzomby
On Mar 6, 10:14 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 06 Mar 2012, at 17:32, meekerdb wrote:
>
> > On 3/6/2012 4:26 AM, Bruno Marchal wrote:
>
> >>> It's a language game.
>
> >> The word "game" is so fuzzy that this says nothing at all. Game
> >> theory is a branch of mathematics.
>
> > But "language" says something. It says mathematics is about
> > description.
>
> Mathematicians search what is language independent, and description
> independent. They don't like when a result depends on the choice of a
> base. Mathematics is more about structures and laws.
>
> Math uses languages, but is not a language, even if it can be used as
> such in physics. But there is more to that.
“Cardinal” numbers with values appear to necessarily use language to
describe the unit being measured or quantified (tons, kilos, etc.)?
Quantitative description.
“In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.” http://mathworld.wolfram.com/OrdinalNumber.html
Are the “ordinal” numbers actually adjectives describing the
relational position in a sequence (first, second,…one-ness, two-ness
etc.)? Are numbers (ordinal) necessarily qualitative descriptions?
Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).
Thanks
Bruno Marchal
On 3/6/2012 12:52 PM, Bruno Marchal wrote:
On 06 Mar 2012, at 17:53, meekerdb wrote:
On 3/6/2012 5:54 AM, Bruno Marchal wrote:That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it in the form of "yes doctor", which means that there exist a level such that my consciousness remains unchanged for a digital functional substitution done at that level.
And then the reasoning shows that the physical universe(s), are not generated by any computation. Computations generated my consciousness, and the physical universe is what my consciousness can predict from the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1 part of arithmetic).
If I had written universes are indirectly generated by computation, would that have reflected your view?
Better.But the presence of the word "generated" might still lead to confusion in this setting. Universe(s) are only observed, It is, or they are the 'natural solution' of the comp diophantine measure problem, which bear on the first person.
The only catch I see is that you wrote "can predict" instead of "must predict". Are you allowing for some agency here? mI allow for agency, but not at that level. Indeed Matter, but matter only, is what the mind cannot act on. But the mind can act on the mind, and agency emerges at higher levels.
Dear Bruno,
Why does it seem that you are tacitly accepting the definition of matter as a "substance" as Descartes did in his substance dualism?
If matter is an appearance (and not a substance), does this not allow a form of "mind acting on matter"?
One only need to consider that the selection process whereby the "next" state in time of a configuration of matter is done by a computation.
A real example of this idea is implemented in the generation of MMORPG games that are very popular. Consider the Bostrom-like question: Since we cannot prove that our physical reality is not a MMORPG virtual world, should we not bet that it actually is?
One test for this question is to consider the upper bounds on the ability to detect differences in features at smaller and smaller scales. If, for example, space-time is "granular" then this would almost certainly prove that our physical world is isomorphic to a MMORPG.
This idea would be compatible with COMP if we can identify the "players of the MMORPG" with the individual Löbian machines.
Given that some very resent observations of ultra-high energy gamma photons indicate that space-time is not granular, we need a more sophisticated theory to get the idea to work.
Does not first person indeterminacy also occur in any kind of displacement of relative position, no matter how small that displacement might be? But we have to consider more than one kind of change. We have to consider relative changes for all possible observables such that the canonical conjugate rule is preserved.No. The reason why "my consciousness" can predict, as opposed to "must predict", is the first person indeterminacy. It is the fact that I cannot know which machine I am, nor which computations executes the relevant states.
We can have partial information set, like, assuming bla-bla-bla, if I am duplicate in {W, M}, I will feel to be in M or in W. That is disjuncts. But by UDA-(step 8 included), I have to say at each instant I will be in u1, u2, u3, u4, ... that is the infinite sequence of programs generating my current state. They all compete in the measure, and "we" can only see the result of that from inside. Here the 1p and its invariance for the delays explains that such "results" never appear in the UD, but is on the border of UD*.
Bruno Marchal
On 06 Mar 2012, at 20:44, Pzomby wrote:
>
>
> On Mar 6, 10:14 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> On 06 Mar 2012, at 17:32, meekerdb wrote:
>>
>>> On 3/6/2012 4:26 AM, Bruno Marchal wrote:
>>
>>>>> It's a language game.
>>
>>>> The word "game" is so fuzzy that this says nothing at all. Game
>>>> theory is a branch of mathematics.
>>
>>> But "language" says something. It says mathematics is about
>>> description.
>>
>> Mathematicians search what is language independent, and description
>> independent. They don't like when a result depends on the choice of a
>> base. Mathematics is more about structures and laws.
>>
>> Math uses languages, but is not a language, even if it can be used as
>> such in physics. But there is more to that.
>
> Bruno:
>
> “Cardinal” numbers with values appear to necessarily use language to
> describe the unit being measured or quantified (tons, kilos, etc.)?
> Quantitative description.
OK.
But it is not valid to infer from this, that mathematics is *about*
description.
On the contrary, mathematicians reason on "models" (realities,
structures), and they use description like all scientists.
mathematical logic is the science which study precisely the difference
between description (theories) and their interpretations (in from of
mathematical structure).
As you mention the notion of cardinal, a discovery here made by
logicians is that the notion of cardinal is relative. A set can have a
high cardinality in one model, and yet admit a bijection with N in
another model.
>
> “In common usage, an ordinal number is an adjective which describes
> the numerical position of an object, e.g., first, second, third,
> etc.” http://mathworld.wolfram.com/OrdinalNumber.html
>
> Are the “ordinal” numbers actually adjectives describing the
> relational position in a sequence (first, second,…one-ness, two-ness
> etc.)?
They can be used for that. But they can be much more than that.
> Are numbers (ordinal) necessarily qualitative descriptions?
Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived experience.
But what you say might make sense in some other contexts.
> Numerals symbolize number position (as in particular instants in the
> sequence of the continuum of time).
OK. But that's quantitative for me, or at least a "3p" type of notion.
Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.
Bruno
Stephen P. King
On 06 Mar 2012, at 19:43, Stephen P. King wrote:
On 3/6/2012 12:52 PM, Bruno Marchal wrote:
On 06 Mar 2012, at 17:53, meekerdb wrote:
On 3/6/2012 5:54 AM, Bruno Marchal wrote:That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
This is not my hypothesis. It might be Fredkin or Schmidhuber hypothesis, but not mine. My hypothesis is the hypothesis that "I am a machine", which is ambiguous, so I put it in the form of "yes doctor", which means that there exist a level such that my consciousness remains unchanged for a digital functional substitution done at that level.
And then the reasoning shows that the physical universe(s), are not generated by any computation. Computations generated my consciousness, and the physical universe is what my consciousness can predict from the mixing of determinacy and 1-indterminacy in the UD* (or sigma_1 part of arithmetic).
If I had written universes are indirectly generated by computation, would that have reflected your view?
Better.But the presence of the word "generated" might still lead to confusion in this setting. Universe(s) are only observed, It is, or they are the 'natural solution' of the comp diophantine measure problem, which bear on the first person.
The only catch I see is that you wrote "can predict" instead of "must predict". Are you allowing for some agency here? mI allow for agency, but not at that level. Indeed Matter, but matter only, is what the mind cannot act on. But the mind can act on the mind, and agency emerges at higher levels.
Dear Bruno,
Why does it seem that you are tacitly accepting the definition of matter as a "substance" as Descartes did in his substance dualism?
[BM]
I precisely don't do that. That's when I use the word "primitive matter" for the aristotelian conception of matter, which is more primary than substantial, but is still primary.
Dear Bruno,
I am trying to be consistent and agree with your explanations but it is difficult. It is not your fault, our natural languages are biased inherently toward certain modalities of thinking to the exclusion of others. I was commenting on your wording, semantics.
If matter is an appearance (and not a substance), does this not allow a form of "mind acting on matter"?
[BM]
In a large sense of that expression.
[SPK]
OK, then does this not contradict what you wrote: " Indeed Matter, but matter only, is what the mind cannot act on." I am trying to understand what you where thinking... I think of matter in terms of its best representation "that whose behavior is best computationally emulated only by itself" - following S. Wolfram's reasoning - it has a fixed point property in this way, but it is not the same fixed point as that of Kleene, it is the fixed point of Brouwer. It is "topological", not "logical". The relation between them is the main feature or 'kernel" of the process dual aspect monism that I advocate.
One only need to consider that the selection process whereby the "next" state in time of a configuration of matter is done by a computation.
[BM]
This does not really work. matter is a question of observable, by machine, and the way you talk leads to the digital physics confusion, with the idea that matter is generated by programs, when matter is seen by programs, due to the first person indeterminacy, which bears on infinities of computations, not just one. They might be a winner program, but that's an open problem in the comp theory.
[SPK]
I am accepting as true the conjecture that there is no "winner program" in any kind of global sense, there are only local optimal winners. In this way I do not suffer from the measure problem. The local optimal winner idea is the same as a "Strategy" that tends to an equilibrium. My reasoning follows the same reasoning of what occurs in the question of whether hypergames are finite or not.
A real example of this idea is implemented in the generation of MMORPG games that are very popular. Consider the Bostrom-like question: Since we cannot prove that our physical reality is not a MMORPG virtual world, should we not bet that it actually is?
[BM]?
[SPK]
Have you seen any virtual reality generating programs and studied how they deal with concurrency problems? Do you understand the concurrency problem? It is basically that computations cannot effectively solve resource allocation problems. You might be blind to this because of your Platonist interpretation of computation and mathematics in general... :-(
Comp precisely entails that we are in infinities of "video games". So we can test if we are at the level zero, or if we are simulated, just by comparing the physics then being infinity of games, which is unique and well defined (the Z and X logics, and their higher order extension) with what we observe.
[SPK]
This is inherently difficult because we can only access finite computational resources to do that test in the physical world and the test requires infinite repetition to yield non-trivial results. This is the measure problem all over again! Do you see how the test by falsification is almost impossible and thus your thesis that COMP is falsifiable is very easy to argue against with weak arguments? I believe that COMP is correct but that it is incomplete, not as a theory per se but in its interpretation. Incompleteness is an inherent property of non-trivial finite theories. We also have to account for the appearance of interactions between the "stuff" of physics! The so-called psycho-physical parallelism.
How do we represent interactions between the games? I conjecture that physics is the interaction between games and all interactions occur as bisimulations between them. (Each game is associated with an infinite number of computations that can implement them as you point out and the "players of the games" and the games themselves are interchangeable.)
One test for this question is to consider the upper bounds on the ability to detect differences in features at smaller and smaller scales. If, for example, space-time is "granular" then this would almost certainly prove that our physical world is isomorphic to a MMORPG.
[BM]
The contrary. Comp a priori makes matter into a continuum. You confuse, like many, comp and digital physics.
[SPK]
I was considering a test case in my example above and did not state this explicitly. I agree with you but was trying to demonstrate an idea with an obviously false example.
I agree that COMP makes matter a continuum, but only in the case of the sum over many disjoint classes of games, similar to the concept of a multiverse in Everett and Dewitt's interpretation of QM. This is faithfully represented by considering orthocomplete lattices as plenums of Boolean algebras. But we have to be cautious in thinking of that idea because there does not exist an a priori order (or pre-order as the truth values are not limited to [0,1}) on the games (we see this explicitly in the case of hypergames and Chu_k spaces).
Within each virtual reality game there is a discrete pixelation which is the substitution level for the generated content of the game. This is what generates the "appearance" of substance. Digital physics does not take the relativity of this into account as it tacitly assumes a lowest upper bound on the computational resources of the "physics", i.e. it only considers one "physics" that is implemented digitally, we see this in Zuse , Schmidhuber and Lloyd's work. COMP assumes the relativity and accounts for it in terms of the substitution level in Yes Doctor, but suffers from problems induced by "classical physics" thinking. (My complaints about teleportation are a reference to this.)
This idea would be compatible with COMP if we can identify the "players of the MMORPG" with the individual Löbian machines.
Given that some very resent observations of ultra-high energy gamma photons indicate that space-time is not granular, we need a more sophisticated theory to get the idea to work.
Not at all. Comp implies high plausibility of the existence of a physical continuum, given that physics becomes an infinite sum of infinite computations, including infinite dovetailing on infinities of fields, including the reals. You are not yet taking into account the role of the first person indeterminacy in the translation of the comp body problem into a measure problem on the whole UD*, I think.
Maybe we have completely different ideas of what "physics" is. For me, "physics" is the content and dynamics of a "common world of experience" that is invariant with respect to transformations (copy and paste operations in and between observers!) of 1p plural "content", aka "diffeomorphisms". It is the "sharable" content in the sense that all observers that believe that they "communicate with each other" (without contradictions!) and their belief is true (in the Bp&p sense) within their shared content. But this only is considering the dynamics, there is also the "stuff" that undergoes these dynamics and the appearences of such must be accounted for. I conjecture (with Vaughan Pratt) that the "stuff" (particles, atoms, electrons, photons, etc.) is faithfully representable as topological spaces (not just as number theoretical relations) and thus the relation between logics and topologies is the same relation as that between minds and bodies. So yes, the mind-body problem does reduce to a body problem in COMP. Pratt points this out in his papers when he mentioned that interactions between minds and bodies is trivial, but interactions between minds (or bodies) is not. This is the concurrency problem (and the measure problem!) that I keep mentioning.
I see "sharing" not as an a priori relation, like set intersection, only but also as the collection of equivalences between observers - which I am considering in terms of games as their 1p content - is it more like an equivalence class as a Category but with natural transformations in addition to endomorphisms. There is a version of this idea in the study of "quantum games" where it has been shown that entanglement generates behavior that, in some limit, is identical to classical "substance exchange" models of interaction without any actual "substance exchange". A similar notion is found in Leibniz' notion of monads but an error in reasoning prevented any progress there.
Consideration of this kind of idea is important if we are to finally disabuse ourselves of the Aristotelian notion of substance.
Does not first person indeterminacy also occur in any kind of displacement of relative position, no matter how small that displacement might be? But we have to consider more than one kind of change. We have to consider relative changes for all possible observables such that the canonical conjugate rule is preserved.No. The reason why "my consciousness" can predict, as opposed to "must predict", is the first person indeterminacy. It is the fact that I cannot know which machine I am, nor which computations executes the relevant states.
We can have partial information set, like, assuming bla-bla-bla, if I am duplicate in {W, M}, I will feel to be in M or in W. That is disjuncts. But by UDA-(step 8 included), I have to say at each instant I will be in u1, u2, u3, u4, ... that is the infinite sequence of programs generating my current state. They all compete in the measure, and "we" can only see the result of that from inside. Here the 1p and its invariance for the delays explains that such "results" never appear in the UD, but is on the border of UD*.
[BM]
We don't have yet any notion of position, so your problem is not yet formalizable in the comp frame. It is premature.
[SPK]
Yes, it may be premature, but conjecture we must or the open problems will never be solved. I wish you would discuss with me the Tennebaum issue that I have mentioned previously. It is part of the reasoning of my conjecture. My main difficulty is that my thinking on this is not in a verbal or symbolic format and so my ability to coherently communicate it is hobbled. It is more a "picture in my head" that I am struggling to communicate...
Onward!
Stephen
Bruno Marchal
I am trying to be consistent and agree with your explanations but it is difficult. It is not your fault, our natural languages are biased inherently toward certain modalities of thinking to the exclusion of others. I was commenting on your wording, semantics.
If matter is an appearance (and not a substance), does this not allow a form of "mind acting on matter"?[BM]In a large sense of that expression.
[SPK]
OK, then does this not contradict what you wrote: " Indeed Matter, but matter only, is what the mind cannot act on." I am trying to understand what you where thinking... I think of matter in terms of its best representation "that whose behavior is best computationally emulated only by itself" - following S. Wolfram's reasoning - it has a fixed point property in this way, but it is not the same fixed point as that of Kleene, it is the fixed point of Brouwer. It is "topological", not "logical". The relation between them is the main feature or 'kernel" of the process dual aspect monism that I advocate.
One only need to consider that the selection process whereby the "next" state in time of a configuration of matter is done by a computation.
[BM]This does not really work. matter is a question of observable, by machine, and the way you talk leads to the digital physics confusion, with the idea that matter is generated by programs, when matter is seen by programs, due to the first person indeterminacy, which bears on infinities of computations, not just one. They might be a winner program, but that's an open problem in the comp theory.
[SPK]
I am accepting as true the conjecture that there is no "winner program" in any kind of global sense, there are only local optimal winners.
In this way I do not suffer from the measure problem.
The local optimal winner idea is the same as a "Strategy" that tends to an equilibrium. My reasoning follows the same reasoning of what occurs in the question of whether hypergames are finite or not.
A real example of this idea is implemented in the generation of MMORPG games that are very popular. Consider the Bostrom-like question: Since we cannot prove that our physical reality is not a MMORPG virtual world, should we not bet that it actually is?[BM]?
[SPK]
Have you seen any virtual reality generating programs and studied how they deal with concurrency problems? Do you understand the concurrency problem?
It is basically that computations cannot effectively solve resource allocation problems. You might be blind to this because of your Platonist interpretation of computation and mathematics in general... :-(
Comp precisely entails that we are in infinities of "video games". So we can test if we are at the level zero, or if we are simulated, just by comparing the physics then being infinity of games, which is unique and well defined (the Z and X logics, and their higher order extension) with what we observe.
[SPK]
This is inherently difficult because we can only access finite computational resources to do that test in the physical world and the test requires infinite repetition to yield non-trivial results. This is the measure problem all over again!
Do you see how the test by falsification is almost impossible and thus your thesis that COMP is falsifiable is very easy to argue against with weak arguments?
I believe that COMP is correct but that it is incomplete, not as a theory per se but in its interpretation. Incompleteness is an inherent property of non-trivial finite theories. We also have to account for the appearance of interactions between the "stuff" of physics! The so-called psycho-physical parallelism.
How do we represent interactions between the games? I conjecture that physics is the interaction between games and all interactions occur as bisimulations between them. (Each game is associated with an infinite number of computations that can implement them as you point out and the "players of the games" and the games themselves are interchangeable.)
[SPK]
One test for this question is to consider the upper bounds on the ability to detect differences in features at smaller and smaller scales. If, for example, space-time is "granular" then this would almost certainly prove that our physical world is isomorphic to a MMORPG.[BM]The contrary. Comp a priori makes matter into a continuum. You confuse, like many, comp and digital physics.
I was considering a test case in my example above and did not state this explicitly. I agree with you but was trying to demonstrate an idea with an obviously false example.
I agree that COMP makes matter a continuum, but only in the case of the sum over many disjoint classes of games, similar to the concept of a multiverse in Everett and Dewitt's interpretation of QM. This is faithfully represented by considering orthocomplete lattices as plenums of Boolean algebras. But we have to be cautious in thinking of that idea because there does not exist an a priori order (or pre-order as the truth values are not limited to [0,1}) on the games (we see this explicitly in the case of hypergames and Chu_k spaces).
Within each virtual reality game there is a discrete pixelation which is the substitution level for the generated content of the game. This is what generates the "appearance" of substance. Digital physics does not take the relativity of this into account as it tacitly assumes a lowest upper bound on the computational resources of the "physics", i.e. it only considers one "physics" that is implemented digitally, we see this in Zuse , Schmidhuber and Lloyd's work.
COMP assumes the relativity and accounts for it in terms of the substitution level in Yes Doctor, but suffers from problems induced by "classical physics" thinking. (My complaints about teleportation are a reference to this.)
This idea would be compatible with COMP if we can identify the "players of the MMORPG" with the individual Löbian machines.
Given that some very resent observations of ultra-high energy gamma photons indicate that space-time is not granular, we need a more sophisticated theory to get the idea to work.
Not at all. Comp implies high plausibility of the existence of a physical continuum, given that physics becomes an infinite sum of infinite computations, including infinite dovetailing on infinities of fields, including the reals. You are not yet taking into account the role of the first person indeterminacy in the translation of the comp body problem into a measure problem on the whole UD*, I think.
[SPK]
Maybe we have completely different ideas of what "physics" is. For me, "physics" is the content and dynamics of a "common world of experience" that is invariant with respect to transformations (copy and paste operations in and between observers!) of 1p plural "content",
aka "diffeomorphisms".
It is the "sharable" content in the sense that all observers that believe that they "communicate with each other" (without contradictions!) and their belief is true (in the Bp&p sense) within their shared content. But this only is considering the dynamics, there is also the "stuff" that undergoes these dynamics and the appearences of such must be accounted for.
I conjecture (with Vaughan Pratt) that the "stuff" (particles, atoms, electrons, photons, etc.) is faithfully representable as topological spaces (not just as number theoretical relations) and thus the relation between logics and topologies is the same relation as that between minds and bodies. So yes, the mind-body problem does reduce to a body problem in COMP. Pratt points this out in his papers when he mentioned that interactions between minds and bodies is trivial, but interactions between minds (or bodies) is not. This is the concurrency problem (and the measure problem!) that I keep mentioning.
I see "sharing" not as an a priori relation, like set intersection, only but also as the collection of equivalences between observers - which I am considering in terms of games as their 1p content - is it more like an equivalence class as a Category but with natural transformations in addition to endomorphisms. There is a version of this idea in the study of "quantum games" where it has been shown that entanglement generates behavior that, in some limit, is identical to classical "substance exchange" models of interaction without any actual "substance exchange". A similar notion is found in Leibniz' notion of monads but an error in reasoning prevented any progress there.
Consideration of this kind of idea is important if we are to finally disabuse ourselves of the Aristotelian notion of substance.
[SPK]
Does not first person indeterminacy also occur in any kind of displacement of relative position, no matter how small that displacement might be? But we have to consider more than one kind of change. We have to consider relative changes for all possible observables such that the canonical conjugate rule is preserved.No. The reason why "my consciousness" can predict, as opposed to "must predict", is the first person indeterminacy. It is the fact that I cannot know which machine I am, nor which computations executes the relevant states.
We can have partial information set, like, assuming bla-bla-bla, if I am duplicate in {W, M}, I will feel to be in M or in W. That is disjuncts. But by UDA-(step 8 included), I have to say at each instant I will be in u1, u2, u3, u4, ... that is the infinite sequence of programs generating my current state. They all compete in the measure, and "we" can only see the result of that from inside. Here the 1p and its invariance for the delays explains that such "results" never appear in the UD, but is on the border of UD*.
[BM]
We don't have yet any notion of position, so your problem is not yet formalizable in the comp frame. It is premature.
Yes, it may be premature, but conjecture we must or the open problems will never be solved.
I wish you would discuss with me the Tennebaum issue that I have mentioned previously. It is part of the reasoning of my conjecture. My main difficulty is that my thinking on this is not in a verbal or symbolic format and so my ability to coherently communicate it is hobbled. It is more a "picture in my head" that I am struggling to communicate...
Pzomby
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.
>
> > “In common usage, an ordinal number is an adjective which describes
> > the numerical position of an object, e.g., first, second, third,
> > etc.” http://mathworld.wolfram.com/OrdinalNumber.html
>
> > Are the “ordinal” numbers actually adjectives describing the
> > relational position in a sequence (first, second,…one-ness, two-ness
> > etc.)?
>
> They can be used for that. But they can be much more than that.
in sport races gives a quality of feeling to the participants,
observers/bettors.
>
> > Are numbers (ordinal) necessarily qualitative descriptions?
>
> Perhaps. In the comp frame, I prefer to ascribe the qualities of
> numbers, by the possible computational relation that they have with
> respect to their most probable universal environment. This is more
> akin with the human conception of quality as being a lived experience.
> But what you say might make sense in some other contexts.
The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process. eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001. In nature: January in central Europe exudes certain
environmental qualitative conditions.
>
> > Numerals symbolize number position (as in particular instants in the
> > sequence of the continuum of time).
>
> OK. But that's quantitative for me, or at least a "3p" type of notion.
> Quality is more 1p, and can be handled at the meta-level by modal
> logic, or by (often non standard) logics.
>
> Bruno
are qualitative.
You state: “Quality is more 1p” but it is not exclusive to 1p. Humans
observe and have empathy for others qualitative conditions and
states.
Pz
Bruno Marchal
On Mar 7, 5:29 am, Bruno Marchal <marc...@ulb.ac.be> wrote:OK.But it is not valid to infer from this, that mathematics is *about*description.On the contrary, mathematicians reason on "models" (realities,structures), and they use description like all scientists.mathematical logic is the science which study precisely the differencebetween description (theories) and their interpretations (in from ofmathematical structure).As you mention the notion of cardinal, a discovery here made bylogicians is that the notion of cardinal is relative. A set can have ahigh cardinality in one model, and yet admit a bijection with N inanother model.Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.
“In common usage, an ordinal number is an adjective which describesthe numerical position of an object, e.g., first, second, third,etc.” http://mathworld.wolfram.com/OrdinalNumber.htmlAre the “ordinal” numbers actually adjectives describing therelational position in a sequence (first, second,…one-ness, two-nessetc.)?They can be used for that. But they can be much more than that.
Yes. Then it is Ok to use it for that. eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.
Are numbers (ordinal) necessarily qualitative descriptions?Perhaps. In the comp frame, I prefer to ascribe the qualities ofnumbers, by the possible computational relation that they have withrespect to their most probable universal environment. This is moreakin with the human conception of quality as being a lived experience.But what you say might make sense in some other contexts.
It is the “lived experience” that is reality as I understand.
The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process. eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001. In nature: January in central Europe exudes certain
environmental qualitative conditions.
Numerals symbolize number position (as in particular instants in thesequence of the continuum of time).OK. But that's quantitative for me, or at least a "3p" type of notion.Quality is more 1p, and can be handled at the meta-level by modallogic, or by (often non standard) logics.Bruno
Duration of time is quantitative. Existing conditions in the duration
are qualitative.
You state: “Quality is more 1p” but it is not exclusive to 1p. Humans
observe and have empathy for others qualitative conditions and
states.
Craig Weinberg
others qualitative conditions, but it does respect their mass,
density, velocity, etc...quantitative (or anti-qualitative) qualities.
Craig
Stephen P. King
On 07 Mar 2012, at 18:36, Pzomby wrote:
On Mar 7, 5:29�am, Bruno Marchal <marc...@ulb.ac.be> wrote:
OK.
But it is not valid to infer from this, that mathematics is *about*
description.
On the contrary, mathematicians reason on "models" (realities,
structures), and they use description like all scientists.
mathematical logic is the science which study precisely the difference
between description (theories) and their interpretations (in from of
mathematical structure).
As you mention the notion of cardinal, a discovery here made by
logicians is that the notion of cardinal is relative. A set can have a
high cardinality in one model, and yet admit a bijection with N in
another model.
Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.
Hmm... OK.
In logic they are symbol associated with axioms and rules, and they have (standard) semantics, for exemple the mathematical "meaning" of + is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2) .... (6,7, 13), ..., (1, 23, 24), ....}.�
Dear Bruno,
��� I could not resist! So they are infinite after all! Umm, where did I see the idea of representing things as equivalence classes... LOL! I wrote of that a while back... Whatever... My apologies, I am in a good mood and being my normal sarcastic self.
�In common usage, an ordinal number is an adjective which describes
the numerical position of an object, e.g., first, second, third,
etc.� �http://mathworld.wolfram.com/OrdinalNumber.html
Are the �ordinal� numbers actually adjectives describing the
relational position in a sequence (first, second,�one-ness, two-ness
etc.)?
They can be used for that. But they can be much more than that.
Yes. Then it is Ok to use it for that. �eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.
OK. But I would say the "quality" of being the first is more in the mind of the machine winning the competition, or in the mind of the machines members of the jury, than in the ordering relation itself.
��� Are these not equivalent in the Platonic sense? After all, we are considering universal machinery that ignores any kind of local gauge symmetry.
Are numbers (ordinal) necessarily qualitative descriptions?
Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived experience.
But what you say might make sense in some other contexts.
It is the �lived experience� that is reality as I understand.
OK. That is the reality of subjective experience, but we can bet there is something independent of that reality, and which might be responsible for that reality.
��� It seems to me that any one that would bet against that "there is something independent of that reality" would be a sucker or a solipsist or some superposition thereof! How does this tie into 1p indeterminancy?
The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process. �eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001. �In nature: January in central Europe exudes certain
environmental qualitative conditions.
Once universal numbers are in relation with other one, many qualitative conditions can happen, assuming digital mechanism.
��� Wait a second, does not digital mechanism assume a fixed substitution level?
Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).
OK. But that's quantitative for me, or at least a "3p" type of notion.
Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.
Bruno
Duration of time is quantitative. �Existing conditions in the duration
are qualitative.
I doubt this. I would bet that if time can be quantitative, and objectively measured by different observers, the duration notion is more qualitative, and subjective.
��� How can a "measure of change" be anything but quantitative? Given that we are seriously considering that all of our 1p and 3p tropes are, literally, nothing more than numbers and relations between them, what else is there?
��� It could be that "qualities" are just spectral ranging over local gauges... THink of how we can associate even an infinite field of continuous transformations with a single point using fiber bundles. I strongly suspect that this is exactly equivalent to "infinite computations running through each 1p"...�
You state: �Quality is more 1p� but it is not exclusive to 1p. �Humans
observe and have �empathy for others qualitative conditions and
states.
I agree.
Onward!
Stephen
Bruno Marchal
On 3/8/2012 1:43 PM, Bruno Marchal wrote:On 07 Mar 2012, at 18:36, Pzomby wrote:Yes, but even the symbols =, +, x, *, are notations that are
substitutes for words. Eg. Equals, addition or union, multiplication.
The operational notations are words used to describe the formulation
of the model.
Hmm... OK.In logic they are symbol associated with axioms and rules, and they have (standard) semantics, for exemple the mathematical "meaning" of + is given by the set {(0,0,0) (0, 1, 1), (1,0, 1) (1,1,2) .... (6,7, 13), ..., (1, 23, 24), ....}.
I could not resist! So they are infinite after all!
Yes. Then it is Ok to use it for that. eg. 1stness, 2ndness, 3rdness
in sport races gives a quality of feeling to the participants,
observers/bettors.
OK. But I would say the "quality" of being the first is more in the mind of the machine winning the competition, or in the mind of the machines members of the jury, than in the ordering relation itself.
Are these not equivalent in the Platonic sense?
After all, we are considering universal machinery that ignores any kind of local gauge symmetry.
Are numbers (ordinal) necessarily qualitative descriptions?
Perhaps. In the comp frame, I prefer to ascribe the qualities of
numbers, by the possible computational relation that they have with
respect to their most probable universal environment. This is more
akin with the human conception of quality as being a lived experience.
But what you say might make sense in some other contexts.
It is the “lived experience” that is reality as I understand.
OK. That is the reality of subjective experience, but we can bet there is something independent of that reality, and which might be responsible for that reality.
It seems to me that any one that would bet against that "there is something independent of that reality" would be a sucker or a solipsist
or some superposition thereof! How does this tie into 1p indeterminancy?
The condition of the universal environment is influenced by an event
at a point in time of the evolutionary process. eg. Certain
qualitative conditions existed in Oct. 1066 in Britain. Also,
9/11/2001. In nature: January in central Europe exudes certain
environmental qualitative conditions.
Once universal numbers are in relation with other one, many qualitative conditions can happen, assuming digital mechanism.
Wait a second, does not digital mechanism assume a fixed substitution level?
Numerals symbolize number position (as in particular instants in the
sequence of the continuum of time).
OK. But that's quantitative for me, or at least a "3p" type of notion.
Quality is more 1p, and can be handled at the meta-level by modal
logic, or by (often non standard) logics.
Bruno
Duration of time is quantitative. Existing conditions in the duration
are qualitative.
I doubt this. I would bet that if time can be quantitative, and objectively measured by different observers, the duration notion is more qualitative, and subjective.
How can a "measure of change" be anything but quantitative?
Given that we are seriously considering that all of our 1p and 3p tropes are, literally, nothing more than numbers and relations between them, what else is there?
You state: “Quality is more 1p” but it is not exclusive to 1p. Humans
observe and have empathy for others qualitative conditions and
states.
I agree.
It could be that "qualities" are just spectral ranging over local gauges... THink of how we can associate even an infinite field of continuous transformations with a single point using fiber bundles. I strongly suspect that this is exactly equivalent to "infinite computations running through each 1p"...
socr...@bezeqint.net
/ Quantum Theory as Quantum Information /
===…
#
Does information begin on the quarks level?
No. Quark cannot leave an atom.
Maybe does proton have quant of information?
No. Single proton has no quant of information.
Why?
Because information can be transfered only by
electromagnetic fields. And we don’t have a theory
about protono-magnetic fields.
#
In our earthly world there is only one fundamental
particle - electron who can transfer information.
Can an electron be quant of information?
Maybe at first glance this seems to be a rather senseless questions.
But . . . . .
Energy is electromagnetic waves (em).
In 1904 Lorentz proved: there isn’t em waves without Electron
It means the source of these em waves must be an Electron
The electron and the em waves they are physical reality
==============
#
1900, 1905
Planck and Einstein found the energy of electron: E=h*f.
1916
Sommerfeld found the formula of electron : e^2=ah*c,
it means: e = +ah*c and e = -ah*c.
1928
Dirac found two more formulas of electron’s energy:
+E=Mc^2 and -E=Mc^2.
According to QED in interaction with vacuum electron’s
energy is infinite: E= ∞
Questions.
Why does the simplest particle - electron have six ( 6 ) formulas ?
Why does electron obey five ( 5) Laws ?
a) Law of conservation and transformation energy/ mass
b) Maxwell’s equations
c) Heisenberg Uncertainty Principle / Law
d) Pauli Exclusion Principle/ Law
e) Fermi-Dirac statistics
#.
What is an electron ?
Now nobody knows
In the internet we can read hundreds theories about electron
All of them are problematical
We can read hundreds books about philosophy of physics.
But how can we trust them if we don’t know what is electron ?
====.
Quote by Heinrich Hertz on Maxwell's equations:
"One cannot escape the feeling that these mathematical formulae
have an independent existence and an intelligence of their own,
that they are wiser than we are, wiser even than their discoverers,
that we get more out of them than was originally put into them."
====.
Ladies and Gentlemen !
Friends !
Electron is not as simple as we think and, maybe, he is wiser than we
are.
==========.
#
We know, there is no information transfer
without energy transfer. More correct: there is no quant
information transfer without quant energy transfer.
And the electron has the least electric charge.
It means it has some quant of the least information.
What can electron do with this information?
Let us look the Mendeleev / Moseley periodic table.
We can see that electron interacts with proton
and creates atom of hydrogen.
This is simplest design, which was created by electron.
And we can see how this information grows and reaches
high informational level. And the most complex design,
which was created by electron is the Man.
The Man is alive essence. Animals, birds, fish are alive essences.
And an atom? And atom is also alive design.
The free atom of hydrogen can live about 1000 seconds.
And someone a long time ago has already said, that if to give
suffices time to atom of hydrogen, he would turn into Man.
Maybe it is better not to search about "dark, virtual particles "
but to understand what the electron is,
because even now nobody knows what electron is.
=======================
In my opinion the Electron is quant of information.
Was I mistaken? No !
Because according to Pauli Exclusion Principle
only one single electron can be in the atom.
This electron reanimates the atom.
This electron manages the atom.
If the atom contains more than one electron
(for example - two), this atom represents " Siamese twins".
Save us, the Great God, of having such atoms, such children!
Each of us has an Electron, but we do not know it.
#
Many years ago man has accustomed some wild
animals (wolf, horse, cat, bull , etc.)
and has made them domestic ones.
But the man understands badly the four-footed friends.
In 1897 J. J. Thomson discovered new particle - electron.
Gradually man has accustomed electron to work for him.
But the man does not understand what an electron is.
By my peasant logic at first it is better to understand
the closest and simplest particle photon /electron and
then to study the far away space and another particles.
==========.
Best wishes.
Israel Sadovnik. Socratus.
=====…
P.S.
Robert Milliken, who measured a charge of electron,
in his Nobel speech ( 1923 ) told, that he knew nothing
about the “last essence of electron”.
#
The verse: The world of electron.
But maybe these electrons are World,
where there are five continents:
the art,
knowledge,
wars,
thrones
and the memory of forty centuries.
/ Valery Brusov./
===============…